发表机构
North-Eastern Hill University; Research Center for Theoretical Physics, Central Visayan Institute Foundation; Linnaeus University; Central Mindanao University（东北丘陵大学; 中维萨亚斯研究所理论物理研究中心; 林奈大学; 棉兰老中央大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究加权Leavitt路代数相关的加权图幺半群的合流性与可消去性，给出对应刻画并证明分次同构关系。
AI 中文摘要
对于行有限加权图$(E,w)$，Preusser证明了加权Leavitt路代数$L_k(E,w)$上有限生成投射模的幺半群$\boldsymbol{\nu}(L_k(E,w))$与组合定义的加权图幺半群$\boldsymbol{M}(E,w)$同构。我们研究$\boldsymbol{M}(E,w)$的两个结构性质：合流性与可消去性。我们在表示$\boldsymbol{M}(E,w)$的自由交换幺半群上引入归约系统，通过构造明确的非合流三元组得到非合流的充分条件，并对某些类别的加权图给出完整的合流性刻画。转向可消去性，我们在满足(LPA)条件的Preusser类加权图中展开研究，这类图对应的$L_k(E,w)$可通过两步构造同构于未加权的Leavitt路代数$L_k(F)$。我们引入与该构造中间步骤相关的辅助图，用其给出$\boldsymbol{M}(E,w)$可消去性的图论刻画。最后，在(LPA)条件下，我们证明Preusser的构造可升级为关于加权Leavitt路代数标准$\boldsymbol{Z}^{\boldsymbol{\nu}(E,w)}$-分次的分次同构$L_k(E,w) \boldsymbol{\text{gr}} L_k(F)$，使得$\boldsymbol{\nu}^{\boldsymbol{\text{gr}}}(L_k(E,w))$作为$\boldsymbol{Z}^{\boldsymbol{\nu}(E,w)}$-幺半群同构于$\boldsymbol{\nu}^{\boldsymbol{\text{gr}}}(L_k(F))$。
英文摘要
For a row-finite weighted graph $(E,w)$, Preusser showed that the monoid $\mathcal{V}(L_k(E,w))$ of finitely generated projective modules over the weighted Leavitt path algebra $L_k(E,w)$ is isomorphic to a combinatorially defined weighted graph monoid $\mathcal{M}(E,w)$. We study two structural properties of $\mathcal{M}(E,w)$: confluence and cancellativity. We introduce a reduction system on the free commutative monoid presenting $\mathcal{M}(E,w)$, obtain sufficient conditions for non-confluence by constructing explicit non-confluent triples, and provide a complete confluence characterization for certain classes of weighted graphs. Turning to cancellativity, we work within Preusser's class of weighted graphs satisfying Condition (LPA), for which $L_k(E,w)$ is isomorphic to an unweighted Leavitt path algebra $L_k(F)$ via a two-step construction. We introduce an auxiliary graph associated to the intermediate step of this construction and use it to give a graph-theoretic characterization of when $\mathcal{M}(E,w)$ is cancellative. Finally, under Condition (LPA), we show that Preusser's construction upgrades to a graded isomorphism $L_k(E,w) \cong_{\operatorname{gr}} L_k(F)$ with respect to the standard $\mathbb{Z}^{λ(E,w)}$-grading of weighted Leavitt path algebras, yielding $\mathcal{V}^{\operatorname{gr}}(L_k(E,w)) \cong \mathcal{V}^{\operatorname{gr}}(L_k(F))$ as $\mathbb{Z}^{λ(E,w)}$-monoids.
Comments23 Pages; comments are welcome
